JP-A-2009-144577 discloses an apparatus for determining failure of a particulate filter. This apparatus includes a particulate filter, an electric insulating material, a plurality of electrodes, and control means. More specifically, the particulate filter is disposed at an exhaust passage of an internal combustion engine. The electric insulating material is disposed downstream of the particulate filter and deposited with particulate matter (PM). The electrodes are disposed, mutually spaced apart from each other, on the electric insulating material. The control means measures an index correlated with an electric resistance value across the electrodes and, when detecting that the measured index is smaller than a predetermined reference value, determines that the particulate filter is faulty.